Finite Group Databasebeta

← #7690002

Subgroups — #7690002

Order 512.

8322 conjugacy classes of subgroups.

The subgroup lattice has 1055 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3497C211yesmaximal, characteristic, complemented
2C2×#3483C211yesmaximal, characteristic, complemented
3#59419C213yesmaximal, complemented
4#59093C216yesmaximal, complemented
5#59039C213yesmaximal, complemented
6#59033C213yesmaximal, complemented
7#45385C216yesmaximal, complemented
8#44885C216yesmaximal, complemented
9#39469C213yesmaximal, complemented
10#38958C213yesmaximal, complemented
11#37780C216yesmaximal, complemented
12Q8×#124C211yesmaximal, characteristic, complemented
13Q8×C22⋊Q8C211yesmaximal, characteristic, complemented
14#36444C211yesmaximal, characteristic, complemented
15#36432C212yesmaximal, complemented
16#36274C213yesmaximal, complemented
17#36149C213yesmaximal, complemented
18#35831C212yesmaximal, complemented
19#35757C212yesmaximal, complemented
20#34715C213yesmaximal, complemented
21#34313C211yesmaximal, characteristic, complemented
22#34259C212yesmaximal, complemented
23C4×#548C211yesmaximal, characteristic, complemented
24C22×2−1+4C2212yes—
25#3497—216no—
26#3483—216no—
27C2×Q82C2211yescharacteristic
28C2×#555C2213yes—
29C2×#555C2216yes—
30C2×#550C2213yes—
31C2×#550C2213yes—
32C2×#550C2212yes—
33C2×#550C2211yescharacteristic
34C2×D4×Q8C2213yes—
35C2×D4×Q8C2211yescharacteristic
36C2×#548C2216yes—
37C2×#548C2212yes—
38C2×#548C2211yescharacteristic
39C2×#548C2212yes—
40C2×#537C2216yes—
41C2×#532C2213yes—
42C2×#532C2213yes—
43C2×#532C2213yes—
44C2×#532C2216yes—
45C2×#520C2212yes—
46C2×C4×#41C2212yes—
47C2×C4×#41C2211yescharacteristic
48C2×C4×#41C2213yes—
49C22×C4×Q8C2211yescharacteristic
50#2862C2213yes—
51#2857C2213yes—
52#2857C2213yes—
53#2855C2216yes—
54#2712C22112yes—
55#2700C22112yes—
56#2700C22112yes—
57#2699C22112yes—
58#2688C22112yes—
59#2686C22112yes—
60#2676C22112yes—
61#2620C2216yes—
62#2615C2216yes—
63#2582C2213yes—
64#2568C2213yes—
65#2567C2213yes—
66#2563C2213yes—
67#2547C2213yes—
68#2544C2216yes—
69#2543C22112yes—
70#2537C2213yes—
71#2537C2216yes—
72#2535C2216yes—
73#2499C2216yes—
74#2492C2216yes—
75#2492C2216yes—
76#2485C2216yes—
77#2476C2216yes—
78#2474C2216yes—
79#2459C2216yes—
80#2456C2216yes—
81#2451C2216yes—
82#2451C2213yes—
83#2450C22112yes—
84#2447C2216yes—
85#2447C2216yes—
86#2447C2216yes—
87#2445C2213yes—
88#2444C22112yes—
89#2440C2216yes—
90#2439C2216yes—
91#2439C2213yes—
92#2438C22112yes—
93#2436C2216yes—
94#2431C2213yes—
95#2431C2216yes—
96#2431C2216yes—
97#2430C22112yes—
98#2428C2216yes—
99#2428C2216yes—
100#2427C2216yes—
101#2427C2216yes—
102#2427C2216yes—
103#2426C2211yescharacteristic
104#2422C2216yes—
105#2420C2216yes—
106#2420C2216yes—
107#2420C2216yes—
108#2420C2213yes—
109#2417C2216yes—
110#2416C2216yes—
111#2415C2216yes—
112#2414C2213yes—
113#2409C2216yes—
114#2407C2216yes—
115#2407C2216yes—
116#2407C2216yes—
117#2407C2213yes—
118#2392C2216yes—
119#2388C2216yes—
120#2367C2213yes—
121#2366C2213yes—
122#2362C2213yes—
123#2361C2216yes—
124#2361C2213yes—
125#2352C2213yes—
126#2351C2211yescharacteristic
127Q8×C4⋊C4C2211yescharacteristic
128Q8×C4⋊C4C2212yes—
129#2349C2216yes—
130D4×C4⋊C4C2213yes—
131#2341C2212yes—
132#2341C2211yescharacteristic
133Q8×C22⋊C4C2212yes—
134Q8×C22⋊C4C2212yes—
135Q8×C22⋊C4C2211yescharacteristic
136Q8×C22⋊C4C2212yes—
137Q8×C22⋊C4C2212yes—
138#2339C2216yes—
139#2339C2216yes—
140#2339C2216yes—
141#2339C2216yes—
142#2339C2216yes—
143#2339C2216yes—
144#2324C2216yes—
145#2311C2216yes—
146#2310C2216yes—
147C4×#127C2213yes—
148C4×#124C2213yes—
149C4×#124C2213yes—
150C4×C22⋊Q8C2213yes—
151C4×C22⋊Q8C2213yes—
152C4×#123C2216yes—
153C4×#121C2213yes—
154C4×#121C2213yes—
155#2297C2216yes—
156C2×#391C2216yes—
157#2293C2213yes—
158C42×Q8C2211yescharacteristic
159C42×D4C2213yes—
160C2×2−1+4—216no—
161C2×2−1+4—216no—
162C2×2−1+4—48no—
163C22×#41C2311yescharacteristic
164C22×#41C2316yes—
165C22×#41C2316yes—
166C22×#41C2316yes—
167C22×#41C2313yes—
168C22×#41C2312yes—
169C22×#41C2316yes—
170C23×Q8C2312yes—
171C23×Q8C2316yes—
172C23×Q8C2311yescharacteristic
173Q82—28no—
174#555—248no—
175#555—224no—
176#550—216no—
177#550—224no—
178#550—224no—
179#550D4116yescomplemented
180D4×Q8—28no—
181D4×Q8—224no—
182#548—216no—
183#548—28no—
184#548—248no—
185#548—48no—
186#537—248no—
187#532—224no—
188#532—224no—
189#532—248no—
190#532—224no—
191C2×C4⋊Q8C2313yes—
192C2×C4⋊Q8C2313yes—
193C2×C4⋊Q8C2313yes—
194C2×C4⋊Q8C2316yes—
195C2×#127C2313yes—
196C2×#127C2316yes—
197C2×#127C2313yes—
198C2×#124C2313yes—
199C2×#124C23112yes—
200C2×#124C2316yes—
201C2×#124C2316yes—
202C2×#124C2316yes—
203C2×#124C2311yescharacteristic
204C2×#124C2316yes—
205C2×#123C2316yes—
206C2×C22⋊Q8C2316yes—
207C2×C22⋊Q8C2313yes—
208C2×C22⋊Q8C2311yescharacteristic
209C2×C22⋊Q8C2316yes—
210C2×C22⋊Q8C23112yes—
211C2×C22⋊Q8C2316yes—
212C2×C22⋊Q8C2316yes—
213C2×#121C2313yes—
214C2×#121C2316yes—
215C2×#121C2316yes—
216C2×#121C2313yes—
217C2×#121C2316yes—
218C2×#121C2311yescharacteristic
219C2×#121C2316yes—
220C2×#121C2316yes—
221C2×#121C23112yes—
222C2×#121C2316yes—
223C2×#121C23112yes—
224C2×#121C2316yes—
225C2×#121C2313yes—
226C2×#121C23112yes—
227C2×#121C2316yes—
228#520—48no—
229C4×#41—216no—
230C4×#41—28no—
231C4×#41—224no—
232C2×C4×Q8—28no—
233C2×C4×Q8C2313yes—
234C2×C4×Q8C2313yes—
235C2×C4×Q8C2311yescharacteristic
236C2×C4×Q8C2312yes—
237C2×C4×Q8C2311yescharacteristic
238C2×C4×Q8C2311yescharacteristic
239C2×C4×Q8C2312yes—
240C2×C4×Q8C2311yescharacteristic
241C2×C4×Q8C2313yes—
242C2×C4×Q8C2311yescharacteristic
243C2×C4×Q8C2311yescharacteristic
244C2×C4×D4C2313yes—
245C2×C4×D4C2316yes—
246C2×C4×D4C2316yes—
247C2×C4×D4C2316yes—
248C2×C4×D4C2316yes—
249C2×C4×D4C2313yes—
250C2×C4×D4C2313yes—
251C2×C4×D4C2313yes—
252C2×C4×D4C2316yes—
253C2×C4×D4C2316yes—
254C2×C4×D4C2316yes—
255C2×C4×D4C2313yes—
256C2×C4×D4C2316yes—
257C2×C4×D4C2316yes—
258C2×C4×D4C2316yes—
259C2×C4×D4C2313yes—
260C2×C4×D4C2316yes—
261C2×C4×D4C2313yes—
262C2×C4×D4C2316yes—
263C2×C4×D4C2313yes—
264C2×#117C2316yes—
265C2×#117C2313yes—
266C2×#117C2313yes—
267C2×#117C2316yes—
268C2×#117C2316yes—
269C22×C4⋊C4C2313yes—
270C22×C4⋊C4C2316yes—
271C22×C42C2316yes—
272C22×C42C2313yes—
273C22×C42C2313yes—
274#400C23112yes—
275#398C23112yes—
276#398C2316yes—
277#397C2316yes—
278#397C23112yes—
279#397C23112yes—
280#397C23112yes—
281#397C23112yes—
282#396C2316yes—
283#396C23112yes—
284#396C2312yes—
285#395C23112yes—
286#395C2316yes—
287#394C23112yes—
288#394C23112yes—
289#394C2312yes—
290#394C2316yes—
291#394C2316yes—
292#394C2316yes—
293#394C2316yes—
294#394C2316yes—
295#394C23112yes—
296#394C23112yes—
297#393C23112yes—
298#393C23112yes—
299#393C2316yes—
300#392C2316yes—
301#392C23112yes—
302#392C23112yes—
303#392C2316yes—
304#392C2316yes—
305#392C2316yes—
306#391C2313yes—
307#391C2316yes—
308#391C23112yes—
309#391C2316yes—
310#391C2316yes—
311#391C2316yes—
312#391C2313yes—
313#391C2316yes—
314#391C2316yes—
315#391C2313yes—
316#391C2316yes—
317#391C2313yes—
318#391C2316yes—
319#391C2316yes—
320#391C2316yes—
321#391C2316yes—
322#391C2316yes—
323#391C2316yes—
324#390C2313yes—
325#390C2316yes—
326#390C2316yes—
327#390C2313yes—
328#390C2316yes—
329#390C2316yes—
330#390C2313yes—
331#390C2313yes—
332#390C2313yes—
333#390C2311yescharacteristic
334#390C2312yes—
335#389C2313yes—
336#389C2316yes—
337#389C2316yes—
338#389C2316yes—
339#389C2313yes—
340#389C2313yes—
341#389C2316yes—
342#389C2316yes—
343#389C2313yes—
344#389C2313yes—
345#389C2311yescharacteristic
346#388C2316yes—
347#388C2316yes—
348#388C2316yes—
349#388C2316yes—
350#388C2316yes—
351#388C2316yes—
352#388C2316yes—
353#388C2312yes—
354#388C2316yes—
355#388C2316yes—
356#387C2316yes—
357#387C23112yes—
358#387C2316yes—
359#387C2316yes—
360#387C2316yes—
361#386C23112yes—
362#386C23112yes—
363#386C23112yes—
364#386C2316yes—
365#386C2316yes—
366#386C2316yes—
367#386C2316yes—
368#386C23112yes—
369#386C23112yes—
370#386C23112yes—
371#386C23112yes—
372#386C2316yes—
373#386C23112yes—
374#386C2316yes—
375#386C2316yes—
376#385C23112yes—
377#385C23112yes—
378#385C23112yes—
379#385C2316yes—
380#385C2316yes—
381#385C2316yes—
382#384C2313yes—
383#384C2316yes—
384#382C2316yes—
385#382C2313yes—
386#382C2313yes—
387#381C23112yes—
388#381C23112yes—
389#381C2316yes—
390#381C23112yes—
391#380C2316yes—
392#380C2316yes—
393#380C2313yes—
394#380C2316yes—
395#380C2316yes—
396#380C2316yes—
397#380C2316yes—
398#380C2316yes—
399#380C2313yes—
400#380C2313yes—
401#380C23112yes—
402#380C2313yes—
403C4×C4⋊C4C2313yes—
404C4×C4⋊C4C2313yes—
405C4×C4⋊C4C2313yes—
406C4×C4⋊C4C2313yes—
407C4×C4⋊C4C2316yes—
408C4×C4⋊C4C2313yes—
409C4×C4⋊C4C2313yes—
410C4×C4⋊C4C2313yes—
411C4×C22⋊C4C2313yes—
412C4×C22⋊C4C2313yes—
413C4×C22⋊C4C2316yes—
414C4×C22⋊C4C2316yes—
415C4×C22⋊C4C2316yes—
416C4×C22⋊C4C2316yes—
417C4×C22⋊C4C2316yes—
418C4×C22⋊C4C2316yes—
419C4×C22⋊C4C2313yes—
420C4×C22⋊C4C2313yes—
421C4×C22⋊C4C2311yescharacteristic
422C4×C22⋊C4C2313yes—
423C2×#95C23112yes—
424C2×#95C23112yes—
425C43C2313yes—
4262−1+4—4128no—
427C2×#41—24no—
428C2×#41—28no—
429C2×#41—24no—
430C2×#41—224no—
431C2×#41—28no—
432C2×#41—24no—
433C2×#41—212no—
434C2×#41—212no—
435C2×#41—224no—
436C2×#41—224no—
437C2×#41—224no—
438C2×#41—224no—
439C2×#41—224no—
440C2×#41—224no—
441C2×#41—412no—
442C2×#41—412no—
443C2×#41—46no—
444C2×#41—412no—
445C2×#41—412no—
446C2×#41—86no—
447C2×#41C2×D4116yes—
448C22×Q8—24no—
449C22×Q8—24no—
450C22×Q8—28no—
451C22×Q8—224no—
452C22×Q8—28no—
453C22×Q8—28no—
454C22×Q8—224no—
455C22×Q8—412no—
456C22×Q8#4118yescomplemented
457C22×Q8C2416yes—
458C22×Q8C2416yes—
459C22×Q8C2413yes—
460C22×Q8C2411yescharacteristic
461C22×Q8C2416yes—
462C22×Q8C2411yescharacteristic
463C22×D4C2411yescharacteristic
464C22×D4C2413yes—
465C22×D4C2416yes—
466C22×D4C2416yes—
467C22×D4C2412yes—
468C22×D4C2416yes—
469C22×D4C2413yes—
470C22×D4C2416yes—
471C22×D4C2413yes—
472C22×D4C2416yes—
473C22×D4C24112yes—
474C22×D4C2416yes—
475C22×D4C2416yes—
476C23×C4C2413yes—
477C23×C4C2413yes—
478C23×C4C2411yescharacteristic
479C23×C4C2416yes—
480C23×C4C2416yes—
481C23×C4C2413yes—
482C23×C4C2416yes—
483C23×C4C24112yes—
484C23×C4C2416yes—
485C23×C4C2413yes—
486C23×C4C2413yes—
487C23×C4C24112yes—
488C4⋊Q8—212no—
489C4⋊Q8—224no—
490C4⋊Q8—212no—
491C4⋊Q8—212no—
492#127—224no—
493#127—212no—
494#127C2×D4124yes—
495#124—212no—
496#124—24no—
497#124—224no—
498#124—224no—
499#124—224no—
500#124—248no—
501#124—412no—
502#123—412no—
503C22⋊Q8—212no—
504C22⋊Q8—24no—
505C22⋊Q8—224no—
506C22⋊Q8—224no—
507C22⋊Q8—248no—
508C22⋊Q8—412no—
509C22⋊Q8—86no—
510#121—212no—
511#121—224no—
512#121—224no—
513#121—224no—
514#121—248no—
515#121—224no—
516#121—248no—
517#121—224no—
518#121—212no—
519#121—24no—
520#121—224no—
521#121—46no—
522#121—412no—
523#121—812no—
524#121C2×D4148yes—
525C4×Q8—24no—
526C4×Q8—24no—
527C4×Q8—28no—
528C4×Q8—24no—
529C4×Q8—24no—
530C4×Q8—28no—
531C4×Q8—212no—
532C4×Q8—24no—
533C4×Q8—212no—
534C4×Q8—212no—
535C4×Q8C2×D418yes—
536C4×D4—212no—
537C4×D4—224no—
538C4×D4—224no—
539C4×D4—224no—
540C4×D4—224no—
541C4×D4—224no—
542C4×D4—224no—
543C4×D4—212no—
544C4×D4—212no—
545C4×D4—224no—
546C4×D4—212no—
547C4×D4—212no—
548C4×D4—412no—
549C4×D4—412no—
550C4×D4—412no—
551C4×D4—46no—
552C4×D4—412no—
553C4×D4—46no—
554C4×D4—86no—
555C4×D4C2×D4124yes—
556#117—224no—
557#117—212no—
558#117—212no—
559#117—224no—
560#117—412no—
561C2×C4⋊C4—212no—
562C2×C4⋊C4—412no—
563C2×C4⋊C4C2413yes—
564C2×C4⋊C4C2416yes—
565C2×C4⋊C4C2413yes—
566C2×C4⋊C4C2416yes—
567C2×C4⋊C4C2413yes—
568C2×C4⋊C4C2412yes—
569C2×C4⋊C4C2416yes—
570C2×C4⋊C4C2413yes—
571C2×C4⋊C4C2416yes—
572C2×C4⋊C4C2413yes—
573C2×C4⋊C4C2413yes—
574C2×C4⋊C4C2416yes—
575C2×C4⋊C4C2416yes—
576C2×C4⋊C4C2413yes—
577C2×C4⋊C4C2413yes—
578C2×C4⋊C4C2413yes—
579C2×C4⋊C4C2411yescharacteristic
580C2×C4⋊C4C2412yes—
581C2×C4⋊C4C2416yes—
582C2×C4⋊C4C2412yes—
583C2×C4⋊C4C2416yes—
584C2×C4⋊C4C2416yes—
585C2×C4⋊C4C2413yes—
586C2×C4⋊C4C24112yes—
587C2×C4⋊C4C2416yes—
588C2×C4⋊C4C2413yes—
589C2×C4⋊C4C2411yescharacteristic
590C2×C22⋊C4C2416yes—
591C2×C22⋊C4C24112yes—
592C2×C22⋊C4C2416yes—
593C2×C22⋊C4C2416yes—
594C2×C22⋊C4C2416yes—
595C2×C22⋊C4C2412yes—
596C2×C22⋊C4C2411yescharacteristic
597C2×C22⋊C4C2411yescharacteristic
598C2×C22⋊C4C24112yes—
599C2×C22⋊C4C2416yes—
600C2×C22⋊C4C2413yes—
601C2×C22⋊C4C2416yes—
602C2×C22⋊C4C2412yes—
603C2×C22⋊C4C2412yes—
604C2×C22⋊C4C2412yes—
605C2×C22⋊C4C2412yes—
606C2×C22⋊C4C2416yes—
607C2×C22⋊C4C2416yes—
608C2×C22⋊C4C2412yes—
609C2×C22⋊C4C2416yes—
610C2×C22⋊C4C2416yes—
611C2×C22⋊C4C2413yes—
612C2×C22⋊C4C2413yes—
613C2×C22⋊C4C2413yes—
614C2×C22⋊C4C24112yes—
615C2×C22⋊C4C2416yes—
616C2×C22⋊C4C2416yes—
617C2×C22⋊C4C24112yes—
618C2×C22⋊C4C2416yes—
619C2×C22⋊C4C2416yes—
620C2×C22⋊C4C2416yes—
621C2×C22⋊C4C2416yes—
622C2×C22⋊C4C2416yes—
623C2×C42—224no—
624C2×C42—212no—
625C2×C42—212no—
626C2×C42C2413yes—
627C2×C42C2416yes—
628C2×C42C2413yes—
629C2×C42C2416yes—
630C2×C42C2413yes—
631C2×C42C2411yescharacteristic
632C2×C42C2412yes—
633C2×C42C2413yes—
634C2×C42C2413yes—
635C2×C42C2413yes—
636C2×C42C2413yes—
637C2×C42C2416yes—
638C2×C42C2413yes—
639C2×C42C2411yescharacteristic
640C2×C42C2413yes—
641C2×C42C2413yes—
642C2×C42C2413yes—
643#95C2413yes—
644#95C2416yes—
645#95C2416yes—
646#95C2416yes—
647#95C2416yes—
648#95C24112yes—
649#95C24112yes—
650#95C24112yes—
651#95C2411yescharacteristic
652#95C2411yescharacteristic
653#95C2412yes—
654#95C2413yes—
655#95C2413yes—
656#95C2413yes—
657#95C2416yes—
658#95C2416yes—
659#95C2416yes—
660#95C2416yes—
661#95C2416yes—
662#95C2416yes—
663#95C2416yes—
664#95C2416yes—
665#95C2416yes—
666#95C2416yes—
667#95C2416yes—
668#95C24112yes—
669C24C2513yes—
670C24C2512yes—
671C24C2516yes—
672C24C2511yescharacteristic
673#41—264no—
674#41—496no—
675#41—496no—
676#41—448no—
677#41—496no—
678#41—416no—
679#41—848no—
680C2×Q8—232no—
681C2×Q8—22no—
682C2×Q8—26no—
683C2×Q8—212no—
684C2×Q8—212no—
685C2×Q8—212no—
686C2×Q8—212no—
687C2×Q8—212no—
688C2×Q8—26no—
689C2×Q8—212no—
690C2×Q8—22no—
691C2×Q8—46no—
692C2×Q8—46no—
693C2×Q8—46no—
694C2×Q8—496no—
695C2×Q8—432no—
696C2×Q8C22×D414yes—
697C2×Q8C2×#41112yes—
698C2×Q8C2×#4114yes—
699C2×Q8H(5,𝔽2)14yes—
700C2×Q82−1+414yescomplemented
701C2×D4—212no—
702C2×D4—212no—
703C2×D4—212no—
704C2×D4—26no—
705C2×D4—24no—
706C2×D4—212no—
707C2×D4—212no—
708C2×D4—224no—
709C2×D4—22no—
710C2×D4—26no—
711C2×D4—24no—
712C2×D4—212no—
713C2×D4—26no—
714C2×D4—212no—
715C2×D4—212no—
716C2×D4—26no—
717C2×D4—26no—
718C2×D4—22no—
719C2×D4—212no—
720C2×D4—26no—
721C2×D4—22no—
722C2×D4—43no—
723C2×D4—43no—
724C2×D4—46no—
725C2×D4—46no—
726C2×D4—46no—
727C2×D4—42no—
728C2×D4—46no—
729C2×D4—46no—
730C2×D4—46no—
731C2×D4—46no—
732C2×D4—46no—
733C2×D4—46no—
734C2×D4—412no—
735C2×D4—46no—
736C2×D4—412no—
737C2×D4C22×D4112yes—
738C2×D4C22×D4124yes—
739C2×D4C22×D4124yes—
740C22×C4—26no—
741C22×C4—212no—
742C22×C4—212no—
743C22×C4—26no—
744C22×C4—212no—
745C22×C4—212no—
746C22×C4—224no—
747C22×C4—22no—
748C22×C4—26no—
749C22×C4—26no—
750C22×C4—26no—
751C22×C4—212no—
752C22×C4—26no—
753C22×C4—224no—
754C22×C4—212no—
755C22×C4—26no—
756C22×C4—212no—
757C22×C4—22no—
758C22×C4—212no—
759C22×C4—26no—
760C22×C4—22no—
761C22×C4—26no—
762C22×C4—26no—
763C22×C4—212no—
764C22×C4—26no—
765C22×C4—412no—
766C22×C4—46no—
767C22×C4—43no—
768C22×C4—46no—
769C22×C4—43no—
770C22×C4—43no—
771C22×C4—412no—
772C22×C4—412no—
773C22×C4—412no—
774C22×C4C22×D4124yes—
775C22×C4C2×#41112yes—
776C22×C4C2511yescharacteristic
777C22×C4C2513yes—
778C22×C4C2513yes—
779C22×C4C2513yes—
780C22×C4C2516yes—
781C22×C4C2511yescharacteristic
782C22×C4C2512yes—
783C22×C4C2516yes—
784C22×C4C2516yes—
785C22×C4C2511yescharacteristic
786C22×C4C2513yes—
787C22×C4C2511yescharacteristic
788C22×C4C2513yes—
789C22×C4C2512yes—
790C22×C4C2513yes—
791C22×C4C2512yes—
792C22×C4C2511yescharacteristic
793C22×C4C2513yes—
794C22×C4C2511yescharacteristic
795C4⋊C4—212no—
796C4⋊C4—26no—
797C4⋊C4—24no—
798C4⋊C4—26no—
799C4⋊C4—212no—
800C4⋊C4—212no—
801C4⋊C4—26no—
802C4⋊C4—26no—
803C4⋊C4—212no—
804C4⋊C4—212no—
805C4⋊C4—26no—
806C4⋊C4—26no—
807C4⋊C4—26no—
808C4⋊C4—212no—
809C4⋊C4—22no—
810C4⋊C4—24no—
811C4⋊C4—26no—
812C4⋊C4—26no—
813C4⋊C4—46no—
814C4⋊C4—42no—
815C4⋊C4—43no—
816C4⋊C4—46no—
817C4⋊C4—46no—
818C4⋊C4—412no—
819C4⋊C4—46no—
820C4⋊C4C22×D4112yes—
821C4⋊C4C22×D414yes—
822C22⋊C4—212no—
823C22⋊C4—224no—
824C22⋊C4—212no—
825C22⋊C4—224no—
826C22⋊C4—22no—
827C22⋊C4—212no—
828C22⋊C4—212no—
829C22⋊C4—24no—
830C22⋊C4—212no—
831C22⋊C4—26no—
832C22⋊C4—212no—
833C22⋊C4—24no—
834C22⋊C4—24no—
835C22⋊C4—24no—
836C22⋊C4—22no—
837C22⋊C4—24no—
838C22⋊C4—46no—
839C22⋊C4—46no—
840C22⋊C4—412no—
841C22⋊C4—43no—
842C22⋊C4—43no—
843C22⋊C4—43no—
844C22⋊C4—42no—
845C22⋊C4—46no—
846C22⋊C4—46no—
847C22⋊C4—46no—
848C22⋊C4—412no—
849C22⋊C4—46no—
850C22⋊C4—46no—
851C22⋊C4—46no—
852C22⋊C4—46no—
853C22⋊C4—46no—
854C22⋊C4C22×D4124yes—
855C42—24no—
856C42—26no—
857C42—22no—
858C42—26no—
859C42—212no—
860C42—26no—
861C42—26no—
862C42—212no—
863C42—26no—
864C42—26no—
865C42—26no—
866C42—212no—
867C42—22no—
868C42—26no—
869C42—43no—
870C42—43no—
871C42C22×D4112yes—
872C23—21no—
873C23—26no—
874C23—26no—
875C23—21no—
876C23—21no—
877C23—26no—
878C23—21no—
879C23—21no—
880C23—26no—
881C23—26no—
882C23—21no—
883C23—26no—
884C23—23no—
885C23—22no—
886C23—23no—
887C23—22no—
888C23—23no—
889C23—22no—
890C23—22no—
891C23—23no—
892C23—22no—
893C23—22no—
894C23—23no—
895C23—23no—
896C23—22no—
897C23—23no—
898C23C23×D4112yes—
899C23C22×#4112yes—
900C23C2611yescharacteristic
901Q8—224no—
902Q8—28no—
903Q8—424no—
904Q8—424no—
905Q8—812no—
906Q8#546116yes—
907D4—248no—
908D4—224no—
909D4—424no—
910D4—424no—
911D4—48no—
912D4—424no—
913D4—424no—
914D4—412no—
915D4—412no—
916D4—44no—
917D4—812no—
918D4—824no—
919D4—812no—
920C2×C4—21no—
921C2×C4—22no—
922C2×C4—23no—
923C2×C4—22no—
924C2×C4—22no—
925C2×C4—23no—
926C2×C4—23no—
927C2×C4—22no—
928C2×C4—23no—
929C2×C4—21no—
930C2×C4—248no—
931C2×C4—224no—
932C2×C4—21no—
933C2×C4—23no—
934C2×C4—21no—
935C2×C4—23no—
936C2×C4—26no—
937C2×C4—26no—
938C2×C4—21no—
939C2×C4—23no—
940C2×C4—21no—
941C2×C4—26no—
942C2×C4—22no—
943C2×C4—21no—
944C2×C4—26no—
945C2×C4—23no—
946C2×C4—26no—
947C2×C4—21no—
948C2×C4—21no—
949C2×C4—21no—
950C2×C4—22no—
951C2×C4—21no—
952C2×C4—23no—
953C2×C4—23no—
954C2×C4—23no—
955C2×C4—21no—
956C2×C4—23no—
957C2×C4—22no—
958C2×C4—26no—
959C2×C4—21no—
960C2×C4—23no—
961C2×C4—23no—
962C2×C4—26no—
963C2×C4—21no—
964C2×C4—23no—
965C2×C4—26no—
966C2×C4—23no—
967C2×C4—26no—
968C2×C4—412no—
969C2×C4—448no—
970C2×C4—424no—
971C2×C4—424no—
972C2×C4—424no—
973C2×C4—412no—
974C2×C4—44no—
975C2×C4—412no—
976C2×C4—86no—
977C2×C4—1612no—
978C2×C4C23×D414yes—
979C2×C4C23×D416yes—
980C2×C4C23×D416yes—
981C2×C4C23×D412yes—
982C2×C4C22×#4116yes—
983C2×C4C22×#4116yes—
984C2×C4C2×H(5,𝔽2)16yes—
985C2×C4C2×2−1+414yes—
986C2×C4C2×2−1+412yes—
987C2×C4#58512yes—
988C2×C4#58512yes—
989C22—212no—
990C22—22no—
991C22—22no—
992C22—212no—
993C22—22no—
994C22—212no—
995C22—41no—
996C22—46no—
997C22—46no—
998C22—41no—
999C22—46no—
1000C22—41no—
1001C22—46no—
1002C22—41no—
1003C22—43no—
1004C22—42no—
1005C22—43no—
1006C22—42no—
1007C22—43no—
1008C22—42no—
1009C22—43no—
1010C22—42no—
1011C22—43no—
1012C22—42no—
1013C22—42no—
1014C22—43no—
1015C22—42no—
1016C22—43no—
1017C22C24×D411yescharacteristic
1018C22C23×#4111yescharacteristic
1019C22C22×H(5,𝔽2)11yescharacteristic
1020C22C22×2−1+411yescharacteristic
1021C22C2×#58511yescharacteristic
1022C22C2×#58511yescharacteristic
1023C22H(7,𝔽2)11yescharacteristic
1024C4—22no—
1025C4—26no—
1026C4—24no—
1027C4—24no—
1028C4—26no—
1029C4—46no—
1030C4—43no—
1031C4—41no—
1032C4—42no—
1033C4—41no—
1034C4—43no—
1035C4—41no—
1036C4—43no—
1037C4—43no—
1038C4—46no—
1039C4—41no—
1040C4—46no—
1041C4C2×#546112yes—
1042C4#348914yes—
1043C2—412no—
1044C2—42no—
1045C2—83no—
1046C2—82no—
1047C2C22×#54611yescharacteristic
1048C2#6279311yescharacteristic
1049C2C2×#348911yescharacteristic
1050C2#6292311yescharacteristic
1051C2#6298711yescharacteristic
1052C2#6299911yescharacteristic
1053C2#6303911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#3497C2semidirect
2. C2×#3483C2semidirect
3. #59419C2semidirect
4. #59093C2semidirect
5. #59039C2semidirect
6. #59033C2semidirect
7. #45385C2semidirect
8. #44885C2semidirect
9. #39469C2semidirect
10. #38958C2semidirect
11. #37780C2semidirect
12. Q8×#124C2semidirect
13. Q8×C22⋊Q8C2semidirect
14. #36444C2semidirect
15. #36432C2semidirect
16. #36274C2semidirect
17. #36149C2semidirect
18. #35831C2semidirect
19. #35757C2semidirect
20. #34715C2semidirect
21. #34313C2semidirect
22. #34259C2semidirect
23. C4×#548C2semidirect
179. #550D4semidirect
456. C22×Q8#41semidirect
700. C2×Q82−1+4semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#34972
C2×#34832
#594192
#590932
#590392
#590332
#453852
#448852
#394692
#389582
#377802
Q8×#1242
Q8×C22⋊Q82
#364442
#364322
#362742
#361492
#358312
#357572
#347152
#343132
#342592
C4×#5482